### Table 1: Symmetric Integer Programs

2007

"... In PAGE 8: ... 5 Computational Experiments In this section, we give empirical evidence of the effectiveness of orbital branching, we investigate the im- pact of choosing the orbit on which branching is based, and we demonstrate the positive effect of orbital fixing. The computations are based on the instances whose characteristics are given in Table1 . The in- stances beginning with cod are used to compute maximum cardinality binary error correcting codes [8], the instances whose names begin with cov are covering designs [15], the instance f5 is the football pool problem on five matches [6], and the instances sts are the well-known Steiner-triple systems [5].... In PAGE 9: ...1. Using branching rule 5, each instance in Table1 was run both with and without orbital fixing. Figure 2 shows a performance profile comparing the results in the two cases.... ..."

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### Table 1: Integer code of the calculator programs.

"... In PAGE 91: ... A program consists of an integer array of a given length. Table1 illustrates the ad-hoc developed integer code. Table 1: Integer code of the calculator programs.... In PAGE 95: ... However, attribute blocks, referenced by the parent pointer of an instantiated symbol, are evaluated at each frame when an instantiated symbol is interpreted. Table1 0: The type TpLsymbol representing a parametric symbol of a rule. Type Field Comment int name The name (number) of the symbol type such as TurtForward, Cylinder, .... ..."

### Table 2 Sizes of Mixed Integer Programs

"... In PAGE 23: ...0. Sizes of the reduced mixed-integer programs, as well as their computational times (in CPU seconds) are given in Table2 . In Table 3 we show the initial (default) solution, the heuristic solution derived from the mixed-integer program (15) - (18), and the optimal solution for each problem we considered.... ..."

### Table 2: Decomposing matrices of mixed integer programs.

"... In PAGE 22: ...nder consideration. The rst interesting case in this context are two blocks and we set := 2. We used := (#rows) 1:05 2 rounded up as the block capacity, which allows a deviation of 10% of the actual block sizes in the decomposition. Table2 shows the results that we obtained for matrices of mixed integer programs taken from the Mipliby and preprocessed with the presolver of the general purpose MIP-solver SIP that is currently under devel- opment at the Konrad-Zuse-Zentrum. We again considered all instances with up to 1,000 rows.... ..."

### Table 1: Decomposing matrices of mixed integer programs.

1997

"... In PAGE 9: ... We used := (#rows) 1:05 2 rounded up as the block capacity, which allows a deviation of 10% of the actual block sizes in the decomposition. Table1 reports the results of our computational experiments for all instances with up to 400 rows. The format is as follows: Column 1 provides the name of the problem, Columns 2 to 4 contain the number of rows, columns and non-zeros of the matrix to be decomposed.... ..."

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### Table 2: Impact of integer program size

2006

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### Table 1: Some applications of integer programming column generation.

2002

"... In PAGE 2: ... This paper is a survey on column generation biased toward solving integer programs. Numerous integer programming column generation applications are described in the literature, as can be seen from Table1 . Generic algorithms for solving problems by integer programming column generation were presented by Barnhart et al.... In PAGE 22: ... 7 Integer Solutions Having introduced decomposition techniques for integer programs in x3, we still need ideas on how to actually obtain integer solutions. The literature is rich on that subject, see Table1 . In fact, X may as well contain non-linear aspects other than discreteness.... ..."

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### Table 3. Computational results for test problems.

"... In PAGE 11: ... Better programs required fewer generations and less computation time. Table3 compares the new encoding method, the penalty encoding method and in- teger programming for the test problems. The left half of Table 3 (a) shows the computa- tional results for the new encoding method and the right half presents for the penalty en- coding method.... In PAGE 11: ... Table 3 compares the new encoding method, the penalty encoding method and in- teger programming for the test problems. The left half of Table3 (a) shows the computa- tional results for the new encoding method and the right half presents for the penalty en- coding method. #8 means that the number of plants is eight, and so on.... In PAGE 11: ... The last three rows show the goal value of the prob- lem, the generation and the time cost in which the goal is attained. Table3 (b) displays the results from using integer programming. According to the schema theorem and the ... In PAGE 12: ... The goal solutions can be thought of as sufficiently good solutions. Table3 shows that the new method requires fewer generations and computation time to produce goal solutions. Table 3 enables the trend line for the number of genera- tions required by the genetic algorithm to be drawn, versus the number of plants.... In PAGE 12: ... Table 3 shows that the new method requires fewer generations and computation time to produce goal solutions. Table3 enables the trend line for the number of genera- tions required by the genetic algorithm to be drawn, versus the number of plants. The gradient of Fig.... In PAGE 13: ... The LINGO package was used to solve these test problems by integer programming. For these cases, LINGO can get feasible solutions only ( Table3 (b)) because the test problems are all highly complex. The com- putational results of this section demonstrate that the new encoding method improves the performance of genetic algorithms by reducing their search space.... ..."